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## 1. The following payoff table shows profit for a decision analysis problem with two decisionalternatives and three sta…

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1. The following payoff table shows profit for a decision analysis problem with two decision

alternatives and three states of nature:

State of Nature

Decision Alternative s1 s2 s3

d1 250 100 25

d2 100 100 75

State of Nature

a. Construct a decision tree for this problem.

b. If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

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2023-03-15T10:00:11+00:00
2023-03-15T10:00:11+00:00 1 Answer
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## Answer ( 1 )

## Please briefly explain why you feel this answer should be reported .

a. Decision Tree:

sql

|———– s1: 250/100 ————|

| |

d1 –| |

| |

|———– s2: 100/100 ————|

| |

| |

Initial |———– s3: 25/75 ————–|

Decision |

———— |

| |

|———– s1: 100/100 ————|

| |

d2 –| |

| |

|———– s2: 100/100 ————|

b.

Optimistic approach: Choose the decision alternative with the highest payoff in the best possible state of nature. In this case, d1 has the highest payoff of 250 in s1. Thus, the recommended decision is d1.

Conservative approach: Choose the decision alternative with the highest payoff in the worst possible state of nature. In this case, d1 has the highest payoff of 25 in s3. Thus, the recommended decision is d1.

Minimax regret approach: Calculate the regret for each decision alternative in each state of nature by finding the difference between the highest payoff for that state of nature and the payoff for that decision alternative in that state of nature. Then, choose the decision alternative with the lowest maximum regret.

lua

|—— s1 —–|—— s2 —–|—— s3 —–|

d1 Regret | 0 | 150 | 225 |

d2 Regret | 150 | 0 | 0 |

The maximum regret for d1 is 225 and the maximum regret for d2 is 150. Thus, the recommended decision is d2.